A school newspaper reporter decides to randomly survey 20 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 23% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.
Part (b)
List the values that X may take on.X = 0, 1, 2, ..., 23 X = 1, 2, 3, ..., 20 X = 1, 2, 3, ..., 23 X = 0, 1, 2, ..., 20
Part (c)
Give the distribution of X.Part (d)
How many of the 20 students do we expect to attend the
festivities? (Round your answer to the nearest whole number.)
student(s)
Part (e)
Find the probability that at most 6 students will attend. (Round your answer to four decimal places.)
Part (f)
Find the probability that more than 4 students will attend. (Round your answer to four decimal places
In: Statistics and Probability
Based on historical data, your manager believes that 34% of the
company's orders come from first-time customers. A random sample of
122 orders will be used to estimate the proportion of
first-time-customers. What is the probability that the sample
proportion is greater than than 0.21?
Note: You should carefully round any z-values you calculate to 4
decimal places to match wamap's approach and calculations.
Answer = (Enter your answer as a number accurate to 4 decimal
places.)
Based on historical data, your manager believes that 32% of the
company's orders come from first-time customers. A random sample of
138 orders will be used to estimate the proportion of
first-time-customers. What is the probability that the sample
proportion is between 0.21 and 0.35?
Note: You should carefully round any z-values you calculate to 4
decimal places to match wamap's approach and calculations.
Answer = (Enter your answer as a number accurate to 4 decimal
places.)
In: Math
Physical activity of obese young adults. In a study on the physical activity of young adults, pediatric researchers measured overall physical activity as the total number of registered movements (counts) over a period of time and then computed the number of counts per minute (cpm) for each subject (International Journal of Obesity, Jan. 2007). The study revealed that the overall physical activity of obese young adults has a mean of μ = 320 cpm μ = 320 cpm and a standard deviation of σ = 100 c p m . σ = 100 c p m . (In comparison, the mean for young adults of normal weight is 540 cpm.) In a random sample of n = 100 n = 100 obese young adults, consider the sample mean counts per minute, ¯ x x ‾ . Describe the sampling distribution of ¯ x x ‾ . What is the probability that the mean overall physical activity level of the sample is between 300 and 310 cpm? What is the probability that the mean overall physical activity level of the sample is greater than 360 cpm?
In: Math
A Monte Carlo simulation is a method for finding a value that is difficult to compute by performing many random experiments.
For example, suppose we wanted to estimate π to within a certain accuracy. We could do so by randomly (and independently) sampling n points from the unit square and counting how many of them are inside the unit circle (assuming that the probability of selecting a point in a given region is proportional to the area of the region). By assuming we actually get the expected number, we can solve for π.
(a) Describe a reasonable sample space to model this experiment.
(b) Let N be the number of sample points that are inside the unit circle. Find E(N).
(c) Use this to construct a random variable P with E(P) = π. This random variable will give your estimate of π.
(d) Find the variance of P.
(e) Use Chebychev’s inequality to find a value of n that guarantees your estimate is within 1/1000 of π with probability at least 50%.
In: Math
Timing-Waiting Lines
Joe Hammer is thinking about setting up a special counter for the do-it-yourself customers at which they can get, not only help where to find products in the store, but also some quick advice about the best way to handle their upcoming projects. Experience has taught Joe that six minutes is a good figure to allow for the average time required to serve a “do-it-yourselfer” and that these customers will arrive every 15 minutes throughout the day.
a.) If joe sets up the counter under these conditions, what operating characteristics might he expect?
b.) What might Joe do to avoid the costs of idleness?
c.) What is the likelihood(probability) that three or more customers will be at the counter, either waiting or being served, at any given time?
Calculate the Utilization rate, idleness rate, Average time in queue, Average time in system, Average number in queue, Average number in system, and probability that three or more customers will be in the counter system at the same time.
In: Operations Management
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An economist studied a large data set of Mexican consumer prices covering episodes of both high and low inflation. One of the goods in the study was coffee. When the inflation rate was low, an average of 3.4 changes in the price of coffee occurred each year. When the inflation rate was high, the price of coffee changed more frequently—an average of 9.2 times each year. [Source: E. Etienne Gagnon, Price setting during low and high inflation: Evidence from Mexico, International Finance Discussion Papers, No. 896 (City: Board of Governors of the Federal Reserve System, 2007).] The expected number of coffee-price changes in a 1-month period is_____
Assume that y, the number of price changes in any 1-month period, is described by a Poisson probability distribution with a mean equal to one of the values you just calculated (depending on whether the inflation rate is high or low). Then x, the number of months between consecutive price changes, is exponentially distributed with a mean of____
If the probability that the price of coffee stays the same for 2 months or less is about 0.44, is Mexico’s inflation rate high or low? a. Low b. High If Mexico is in a high inflation episode, the variance of x is____
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In: Statistics and Probability
1. The sample space contains 5 As and 7 Bs. What is the probability that a randomly selected set of 2 will include 1 A and 1 B?
2. In a city of 120,000 people there are 20,000 Norwegians. What is the probability that a randomly selected person from the city will be Norwegian
4. A corporation receives a particular part in shipments of 100. Research indicated the probabilities shown in the accompanying table for numbers of defective parts in a shipment.
a. What is the probability that there will be fewer than three defective parts in a shipment?
b. What is the probability that there will be more than one defective part in a shipment?
c. The five probabilities in the table sum to 1. Why must this be so?
5. The probability of A is 0.60, the probability of B is 0.40, and the probability of either is 0.76. What is the probability of both A and B
Market research in a particular city indicated that during a week, 18% of all adults watch a television program oriented to business and financial issues, 12% read a publication oriented to these issues, and 10% do both.
a. What is the probability that an adult in this city who watches a television program oriented to business and financial issues reads a publication oriented to these issues?
b. What is the probability that an adult in this city who reads a publication oriented to business and financial issues watches a television program oriented to these issues?
9. At the beginning of winter, a homeowner estimates that the probability is 0.4 that his total heating bill for the three winter months will be less than $380. He also estimates that the probability is 0.6 that the total bill will be less than $460.
a. What is the probability that the total bill will be between $380 and $460?
b. Given no further information, what can be said about the probability that the total bill will be less than $400?
10. Let the random variable X follow a normal distribution with m = 80 and s2 = 100.
a. Find the probability that X is greater than 60.
b. Find the probability that X is greater than 72 and less than 82.
c. Find the probability that X is less than 55.
d. The probability is 0.1 that X is greater than what number?
e. The probability is 0.6826 that X is in the symmetric interval about the mean between which two numbers?
11. Below the age 35, who are infected by Covid-19, there is a 0.8 probability of success in surviving and recovering (This often depended on the health background status of the person).
Calculate the probability of the recovering successes of 7 people in 10 infected aged below 35.
12. The internet connection failures (disconnections) happened with an average of 3 failures every twenty minutes in a day based on a Poisson distribution, calculate the probability of no more disconnections in a day.
13. On weekdays, a bus arrives at the bus top every 20 minutes between 8 a.m. and 10 p.m. Passengers arrive at the bus stop at random times. The time that a person waits is uniformly distributed from 0 to 20 minutes.
In: Statistics and Probability
PART A:
Arrange the elements in decreasing order of first ionization energy.
Rank from highest to lowest first ionization energy. To rank items as equivalent, overlap them.
In, Ge, Se, Cs
PART B:
Arrange the elements in order of decreasing first ionization energy. Rank from highest to lowest first ionization energy. To rank items as equivalent, overlap them.
element x (radius (pm): 110)
element y (radius (pm): 199)
element z (radius (pm): 257)
In: Chemistry
Protein X has a Kd of 0.25 micromolar; protein Y has a Kd of 0.5 micromolar, and protein Z has a Kd of 0.75 micromolar for ligand A. Which one of the following is true?
Group of answer choices
1-Protein X has the highest affinity for ligand A.
2-Protein Z has the highest affinity for ligand A.
3-Protein X has the lowest affinity for ligand A.
4-Protein Y affinity for ligand A is higher than that of protein X.
In: Biology
6.)How much energy is required to excite a hydrogen atom's electron from n=2 to n=5?
Enter your answer with 2 significant figures.
Note: Your answer is assumed to be reduced to the highest power possible.
6 b.) Calculate the wavelength of light that is required to excite
a hydrogen atom's electron from n=2 to n=5?
Enter your answer in meters with 2 significant figures.
Note: Your answer is assumed to be reduced to the highest power possible.
In: Chemistry